The Cultural Side Of Things
An opera-house has 8 lead singers available for a simultaneous performance of 5 operas. Each opera requires 1 lead singer and no lead singer can appear in more than 1 opera.
How many ways can lead singers be assigned to operas? Assume that if singer A is assigned to opera C and singer B is assigned to opera D, that is different than A being assigned to D and B assigned to C, even if the other three operas have identical lead singers in both arrangements.
The answer is 6720.
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1 solution
Moderator note:
Simple standard approach.
The first opera can have any of the 8 singers assigned. Then the second opera can have any of the 7 remaining, etc.
So the number of choices is 8 * 7 * 6 * 5 * 4 = 6720